First of all thank you for your answer.

I am working on an open shop scheduling problem and I need to find  in each stap a maximum number of operations to be executed simultaneously where the lenght of the longest operation is minimized.

I did not try to apply Ford-Fulkerson min cut/max flow approach. I will try to solve it with this approch.

@Sir Christian Sohler

When we remove the k longest edges, we could not find always a matching of cardinality C.

In this paper " Classical and new heuristics for the open-shop problem: A computational evaluation. Christelle Guéret,Christian Prins 1998" (link below), it is said that " this problem can be solved by determining in G successive augmenting paths of maximum capacity (min-max paths). This can be achieved

using avariant of Dijsktra's algorithm for computing paths of maximum capacity,by basically replacing the operator `+' by `max'." 

But this variante of Dijsktra's algorithm calculate an augmenting path where the lenght of the longest edge is minimized and this dont give always a matching where the  lenght of the longest edge is minimized.

Exemple: x1 5 x2 6 x3 2 x4 4 x5 4 x6

x1 3 x2 7 x3 1 x4 4 x5 3 x6 (xi are vertices and the number between are the lenght of the edges)

So for the first augmenting path the lenght of the longest edge is minimized = 6 but for the matching ({ x1 ,x2}, { x3 ,x4}, { x5 ,x6})  is 5 however  for the second augmenting path the lenght of the longest edge is 7 but for the matching ({ x1 ,x2}, { x3 ,x4}, { x5 ,x6}) is 3.

So waht do you think

http://www.sciencedirect.com/science/article/pii/S0377221797003329

@ Sir Christian Sohler

But we need to prove that this method gives always the optimal solution.

And what do you think about the use of the varainte  of Dijsktra's algorithm?

Thank you Sir for your answer